Topology optimization of 2D in-plane single mass MEMS gyroscopes

In this paper, we apply the topology optimization method to the design of MEMS gyroscopes, with the aim of supporting traditional trial and error design procedures. Using deterministic, gradient-based mathematical programming, the approach is here applied to the design of 2D in-plane single mass MEMS gyroscopes. We first focus on a benchmark academic case, for which we present and compare three different formulations of the optimization problem, considering typical industrial requirements. These include the maximization of the response of the sensor’s structure to the external angular rate, target resonant frequencies and minimum or constrained material usage. Also, a minimum length scale is imposed to the geometric features in order to ensure manufacturability, and an explicit penalization of grey elements is proposed to improve convergence to black and white layouts. Once the suitability of the method has been assessed, the formulation associated with the lowest computational cost, i.e. the one considering static estimations of the resonant frequencies, is applied to the design of a real-world MEMS gyroscope, targeting different resonant frequencies.